      In summary, we show that near horizon analysis is a general and simpler method to calculate pole-skipping points. It can not only be applied to AdS spacetime, but also to Lifshitz and Rindler geometry. The pole-skipping points are related to the hydrodynamic dispersion relations in Lifshitz geometry. we calculate the lower-half \(\omega \) -plane pole-skipping points of tensor and Maxwell fields in the anisotropic system near Lifshitz points. The frequencies of these special points are located at \(\mathfrak {w}_{n}=-in\)  with \(n\)  integers. To verify our results, we compare them with outcomes of the AdS\(_4\)  black brane solution in ref.[1]}, [2]} when setting \(z=1\) , \(\theta =0\)  and \(\phi =1\) . They are the same at the first order pole-skipping point (\(\mathfrak {w}_{n}=-i\) ). The momenta \(k_n\)  of higher order pole-skipping points are in the complex \(k\) -plane and we plot the dispersion relations in terms of dimensionless variables \(\frac{\omega }{2\pi T}\)  and \(\frac{\vert k\vert }{2\pi T}\)  . We find that the hydrodynamic dispersion relations pass through pole-skipping points \((\mathfrak {w}_{n}, \vert \mathfrak {k}_{n}\vert )\)  at very small momentum and frequency. For the hydrodynamic analysis, we just consider the linearized perturbation along the \(x\) -direction of tensor mode which translational symmetry is not broken and momentum is not dissipated \((a=0)\)  and of Maxwell vector mode which current is conserved.
